{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*NaH dissociation curve using VQE with UCCSD*_\n",
    "\n",
    "This notebook demonstrates using the Qiskit Chemistry to plot graphs of the ground state energy of the Sodium Hydride (NaH) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the NumPyMinimumEigensolver.\n",
    "\n",
    "_*Note: this molecule is larger than the similar LiH and this notebook can take a while to run.*_\n",
    "\n",
    "This notebook has been written to use the PYSCF chemistry driver."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab\n",
    "\n",
    "from qiskit_nature.second_q.drivers import PySCFDriver\n",
    "from qiskit_nature.second_q.transformers import FreezeCoreTransformer\n",
    "from qiskit_nature.second_q.formats import MoleculeInfo\n",
    "from qiskit_nature.second_q.mappers import ParityMapper\n",
    "from qiskit_nature.second_q.algorithms import GroundStateEigensolver\n",
    "\n",
    "from qiskit_algorithms import NumPyMinimumEigensolver\n",
    "\n",
    "from qiskit_algorithms.optimizers import SLSQP\n",
    "\n",
    "from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD\n",
    "from qiskit_algorithms import VQE\n",
    "from qiskit.primitives import Estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithms = ['NumPyMinimumEigensolver', 'VQE']\n",
    "\n",
    "distances  = [x * 0.1  for x in range(10, 25)]\n",
    "distances += [x * 0.25 for x in range(10, 19)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_energies(algorithm, distances):\n",
    "    print(f'{algorithm}, processing step __', end='')\n",
    "\n",
    "    energies = []\n",
    "    hf_energies = []\n",
    "    estimator = Estimator()\n",
    "\n",
    "    for i, d in enumerate(distances):\n",
    "        print('\\b\\b{:2d}'.format(i), end='', flush=True)\n",
    "\n",
    "        info = MoleculeInfo([\"H\", \"Na\"], [(0.0, 0.0, 0.0), (0.0, 0.0, d)])\n",
    "        driver = PySCFDriver.from_molecule(info, basis=\"sto3g\")\n",
    "        molecule = driver.run()\n",
    "        transformer = FreezeCoreTransformer()\n",
    "        molecule = transformer.transform(molecule)\n",
    "        hamiltonian = molecule.hamiltonian.second_q_op()\n",
    "        mapper = ParityMapper(num_particles=molecule.num_particles)\n",
    "        tapered_mapper = molecule.get_tapered_mapper(mapper)\n",
    "        qubit_op = tapered_mapper.map(hamiltonian)\n",
    "\n",
    "        if algorithm == 'NumPyMinimumEigensolver':\n",
    "            algo = NumPyMinimumEigensolver()\n",
    "            algo.filter_criterion = molecule.get_default_filter_criterion()\n",
    "            solver = GroundStateEigensolver(mapper, algo)\n",
    "            result = solver.solve(molecule)\n",
    "            hf_energies.append(result.hartree_fock_energy)\n",
    "            energies.append(result.total_energies[0])\n",
    "\n",
    "        elif algorithm == 'VQE':\n",
    "            optimizer = SLSQP(maxiter=10000, ftol=1e-9)\n",
    "            ansatz = UCCSD(\n",
    "                molecule.num_spatial_orbitals,\n",
    "                molecule.num_particles,\n",
    "                tapered_mapper,\n",
    "                initial_state=HartreeFock(\n",
    "                    molecule.num_spatial_orbitals,\n",
    "                    molecule.num_particles,\n",
    "                    tapered_mapper,\n",
    "                ),\n",
    "            )\n",
    "            vqe = VQE(estimator, ansatz, optimizer)\n",
    "            vqe.initial_point = [0] * ansatz.num_parameters\n",
    "            algo = GroundStateEigensolver(tapered_mapper, vqe)\n",
    "            result = algo.solve(molecule)\n",
    "            energies.append(result.total_energies[0])\n",
    "            hf_energies.append(result.hartree_fock_energy)\n",
    "\n",
    "    print(' --- complete')\n",
    "    return hf_energies, energies\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPyMinimumEigensolver, processing step 23 --- complete\n",
      "VQE, processing step 23 --- complete\n"
     ]
    }
   ],
   "source": [
    "# took 11 minutes to me\n",
    "hf_energies, npme_energies = compute_energies('NumPyMinimumEigensolver', distances)\n",
    "_, vqe_energies = compute_energies('VQE', distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1c7b6ddde0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n",
    "pylab.plot(distances, npme_energies, label='NumPyMinimumEigensolver')\n",
    "pylab.plot(distances, vqe_energies, label='VQE')\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('NaH Ground State Energy')\n",
    "pylab.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HF bond distance: 1.70 A, energy: -160.315 Ha\n",
      "VQE bond distance: 1.70 A, energy: -160.327 Ha\n",
      "NumpyMinimumEigensolver bond distance: 1.70 A, energy: -160.327 Ha\n"
     ]
    }
   ],
   "source": [
    "print(f\"\"\"HF bond distance: {distances[hf_energies.index(min(hf_energies))]:.2f} A, energy: {min(hf_energies):.3f} Ha\n",
    "VQE bond distance: {distances[vqe_energies.index(min(vqe_energies))]:.2f} A, energy: {min(vqe_energies):.3f} Ha\n",
    "NumpyMinimumEigensolver bond distance: {distances[npme_energies.index(min(npme_energies))]:.2f} A, energy: {min(npme_energies):.3f} Ha\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1c7b2891b0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.plot(distances, np.subtract(np.array(hf_energies), np.array(npme_energies)), label='Hartree-Fock')\n",
    "pylab.plot(distances, np.subtract(np.array(vqe_energies), np.array(npme_energies)), label='VQE')\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('Energy difference from NumPyMinimumEigensolver')\n",
    "pylab.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qiskit==1.1.0\n",
      "qiskit-aer==0.14.2\n",
      "qiskit-algorithms==0.3.0\n",
      "qiskit-ibm-runtime==0.25.0\n",
      "qiskit-machine-learning==0.7.2\n",
      "qiskit-nature==0.7.2\n",
      "qiskit-nature-pyscf==0.4.0\n",
      "qiskit-qasm3-import==0.5.0\n",
      "qiskit-transpiler-service==0.4.5\n"
     ]
    }
   ],
   "source": [
    "! pip freeze | grep qiskit"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
